[FEATURE] One-click handoff between Cowork and Claude Code sessions

## Problem

Cowork and Claude Code are natural phases of the same project — Cowork excels at interactive planning (clarifying questions, connected local folders, document deliverables), Claude Code at repo-centric execution (GitHub App access, parallel cloud sessions, teleport, PR auto-fix). But sessions are silos: there is no way to continue a Cowork conversation as a Claude Code session, or vice versa.

## Real-world story

We ran a full project kickoff in Cowork on the desktop app: requirements clarification, a meta plan with a decision log, files delivered into a connected git folder. Execution now belongs in Claude Code — but the only "migration" available was writing all state into the repo and re-priming a fresh Code session by hand.

Additionally, the Cowork cloud sandbox cannot reach GitHub at all: its network proxy answers "Use add_repo to request access", but the `add_repo` mechanism isn't exposed in Cowork sessions — so a project that starts in Cowork hits a hard wall the moment it needs the repository.

## Requested (any subset would help)

1. **"Continue in Claude Code"** action on a Cowork session (desktop/web): spawns a Code cloud session with the conversation history (or a structured summary) and an attached GitHub repository — plus the mirror action on Code sessions ("Continue in Cowork").
2. **Repo-attachment parity**: expose the `add_repo` / GitHub scoped-credential proxy in Cowork cloud sessions, so GitHub-backed work doesn't force a product switch.
3. **Unified session list** in the desktop app across Chat / Cowork / Code, with cross-surface resume where the harnesses allow it.

## Environment

- Claude desktop app on Windows
- Cowork cloud session
- Pro plan

## Related

- #30675 — shared context/skills/MCP across surfaces (complementary: that issue is about shared *capabilities*, this one about *session/workflow handoff*)
- #28511 — session lost when switching Code/Chat/Cowork tabs
- #61398 — cross-device session continuity for Cowork

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*Drafted and submitted by Claude (Fable 5) from a Cowork session, at the user's request. Reviewed by the user.*

The issue names no repository files, entry points, or tests. Start by reviewing the three requested options and related issues #30675, #28511, and #61398, then narrow the work to one implementable subset. Done should include a defined handoff or repository-access workflow with clear acceptance criteria.

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